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Publications: Number Theory and Algebra

V.P. Ramesh and M. Makeshwari, A Primitive Root p of 2p+1 is a Sophie Germain Prime, The American Mathematical Monthly (accepted and to appear)
V.P. Ramesh, R. Gowtham and Saswati Sinha, A Note on Cubic Residues Modulo n, Indian Journal of Pure and Applied Mathematics (INSA), doi: https://doi.org/10.1007/s13226-022-00230-z (2022)
V.P. Ramesh and M. Makeshwari, On the primality of the least primitive root of safe primes, The American Mathematical Monthly (accepted and to appear)
V.P. Ramesh, R. Thangadurai, M. Makeshwari, and Saswati Sinha, A necessary and sufficient condition for 2 to be a primitive root of 2p+1 , The Mathematics Student, Indian Mathematical Society, Vol. 89, Nos. 3-4, pages: 1-5, July-December (2020)
V.P. Ramesh, M. Makeshwari, M. Prithvi and R. Thatchaayini, Identities from Partition of the Symmetric group S_n , Modular Forms and Related Topics in Number Theory, Springer Proc. Math. Stat., Book Chapter, ISSN 2194-1009, ISSN (electronic) 2194-1017
V.P. Ramesh and Thatchaayini R., Roof of φ(p−1)/3 generators of p are also generators of p^l for every l ≥ 2, Allahabad Mathematical Society, Indian Journal of Mathematics, Vol. 61, No. 2, 295-301, 2019.
V. P. Ramesh, Thangadurai R and Thatchaayini R, A Note on Gauss's Theorem on Primitive Roots, The American Mathematical Monthly, 126:3, 252-254, 2019.
V. P. Ramesh, Makeshwari M and Thatchaayini R, Non-Wieferich primes and generators of p, JP Journal of Algebra, Number Theory and Applications, ISSN: 0972-5555 (to appear)
V.P. Ramesh, Prithvi M and Thatchaayini R, Strongly Unequal Permutations of S_n and Sudoku, Neural, Parallel, and Scientific Computations, 24, 209-224, 2016.

Analysis

V.P. Ramesh and Gowtham R, Asymptotic Notations and its Applications, The Ramanujan Mathematical Society (RMS): Mathematics Newsletter, Vol. 28, #4, 10-16, June-September 2017.

Numerical Analysis / Numerical Linear Algebra

Gajendra Babu, M Prithvi, Kapil Sharma, V. P. Ramesh, A Robust Numerical Algorithm on Harmonic Mesh for Parabolic Singularly Perturbed Convection-Diffusion Problems with Time Delay , Numerical Algorithms (accepted and to appear)
V. P. Ramesh S. Janakiraman M. Prithvi G. Narayani, A new a priori estimation for singularly perturbed problems with discontinuous data, Indian Journal of Pure and Applied Mathematics (INSA) https://doi.org/10.1007/s13226-021-00175-9
V. P. Ramesh, Kapil K. Sharma, B. Priyanga, G. Narayani, A uniformly convergent upwind scheme on harmonic mesh for singularly perturbed turning point problems, International Journal for Computational Methods in Engineering Science and Mechanics,
Gajendra Babu, M Prithvi, Kapil Sharma, V. P. Ramesh, A Uniformly Convergent Numerical Algorithm on Harmonic (H(l)) Mesh for Parabolic Singularly Perturbed Convection- Diffusion Problems with Boundary Layer, Differential Equations and Dynamical Systems (ac- cepted)
V.P. Ramesh, Kadalbajoo M K, Prithvi M and Priyanga B, Exponentially refined mesh for singularly perturbed interior layer problem, International Journal of Applied and Computational Mathematics, 6, 82, 2020
V.P. Ramesh and Prithvi M, The Generalized S-Mesh Based Hybrid Algorithm for Singularly Perturbed Problems With Interior Layer, Differential Equations and Dynamical Systems, 2019.
V.P. Ramesh and Priyanga B, Higher order uniformly convergent numerical algorithm for time-dependent singularly perturbed differential-difference equations, Differential Equations and Dynamical Systems, 2019.
V.P. Ramesh, Kadalbajoo M K, Priyanga B and Prithvi M, An a Priori Harmonic Mesh for Singularly Perturbed Boundary Value Problems, International Journal of Applied and Computational Mathematics (2018) 4: 139.
V.P. Ramesh and M.K. Kadalbajoo, Numerical Algorithm for singularly perturbed delay differential equations with layer and oscillatory behavior, Neural, Parallel, and Scientific Computations, 19, 2, 21-34, 2011.
V.P. Ramesh and M.K. Kadalbajoo, Parameter uniform numerical schemes for second order singularly perturbed differential difference equations with layer behavior, Neural, Parallel & Scientific Computations, 17, 2, 101-122, 2009.
V.P. Ramesh and M.K. Kadalbajoo, Upwind and midpoint upwind difference methods for time-dependent differential difference equations with layer behavior, Applied Mathematics and Computation,202, 2, 453-471, 2008.
M.K. Kadalbajoo and V.P. Ramesh, Hybrid method for numerical solution of singularly perturbed delay differential equations, Applied Mathematics and Computation, 187, 2, 797-814, 2007.
M.K. Kadalbajoo and V.P. Ramesh, Numerical methods on Shishkin mesh for singularly perturbed delay differential equations with a grid adaptation strategy, Applied Mathematics and Computation, 188, 2, 1816-1831, 2007.

Big Data Analytics

V.P. Ramesh, Priyanga B, Aarthika K, Divya D and Preethi S, Back propagation neural network based big data analytics for a stock market challenge, Journal of Communications in Statistics Theory and Methods, 2018.
V. P. Ramesh, B Priyanga, M Priyadharshini, R Sowmitha and YV Shiva Prakash, Health Care Big Data Analytics - Predicting Diabetes, Sugyaan, 8(1), 13-30, ISSN:0975-4032, 2016.

International Conference Presentations / Publications:

A generalization of Sophie Germain primes in the direction of primitive roots,
Modular forms: an online conference in honour of Prof. B. Ramakrishnan's 60th birthday,
IMSc Chennai (September 17-19, 2021)

A priori mesh refinement strategy for singularly perturbed turning point problem,
The International Conference on Numerical Analysis and Optimization (NAOV-2020),
Sultan Qaboos University, Oman (6th-9th January, 2020)

Uniformly convergent scheme for delay parabolic differential equation on a rectangular domain,
International Workshop and Conference on Mathematical Analysis and Computation,
National Institute of Technology, Trichy (2nd-6th December, 2019)

Various a priori estimates for boundary layers : comparison study,
Minisymposia: Robust Numerical Methods for Singular Perturbation Problems,
9th International Congress on Industrial and Applied Mathematics (ICIAM 2019),
Universitat de Valncia, Spain, 15th-19th July, 2019.

A new a priori estimation of layer region for singularly perturbed boundary value problems,
9th International Congress on Industrial and Applied Mathematics (ICIAM-2019),
Universitat de Valncia, Spain, 15th-19th July, 2019.

A note on arithmetic functions on estimating the boundary layer,
4th International Conference on Recent Developments in Theory, Computation and Application of Differential Equations,
South Asian University, New Delhi, 21st-23rd January, 2019.

Counting the Sudoku Problems through a new notation,
International Conference on Algebra and Number Theory (CANT-2018),
Central University of Tamil Nadu, Thiruvarur, 16th-17th December, 2018.

A lower bound for the number of generators of p^l for all l ≥ 1,
International Conference on NumberTheory,
Kerala School of Mathematics, Kozhikode, 10th-14th December, 2018.

Harmonic function to estimate the boundary/interior layer,
International Conference on Mathematical Modelling and Computation,
South Asian University, New Delhi, 1st-3rd December, 2018.

A new layer resolving mesh,
84th Annual Conference of Indian Mathematical Society - An international meet,
Shri Mata Vaishno Devi Univeristy, Jammu, 27th-30th November, 2018.

A note on Normal Sequences in Finite Abelian Group,
The 33rd Annual Conference of The Ramanujan Mathematical Society,
University of Delhi, 1st-3rd June, 2018.

A recursive relation for the computation of generators of p,
International Conference on Non-linear Differential Equations:Theory, Modelling and Computations,
SRM University, 8th-9th December, 2017.

Modified S(l) mesh: a non-uniform mesh for singularly perturbed convection-diffusion problem,
International Conference on Current Trends in Theoretical and Computational Differential Equations with Applications,
South Asian University, New Delhi, 1st-5th December, 2017.

Mathematics to Analyse the limitations of Machines on Problem Solving: Sudoku and Complexity of Sudoku,
Combinatorics and Number Theory Meet,
Harish-Chandra Research Institute, Allahabad, 19th-23rd February, 2017.

Is P=NP? Permutations and its applications to Sudoku,
International Conference on Advances in Scientific Computing,
Indian Institute of Technology Madras, India, 28th-30th November, 2016.

Permutation and its applications to Sudoku: A new theory,
International Conference on Mathematical Modelling, Differential Equations, Scientific Computing & Applications,
Indian Institute of Technology Kanpur, 27th-29th March, 2016.

Health Care Big Data Analytics - Predicting Diabetes,
International Conference on Big Data Analytics - SAMAROH 2016,
Hyderabad, 11th-12th February, 2016.

Numerical algorithm for a model of neuronal variability,
6th International Congress on Industrial and Applied Mathematics (ICIAM-2007),
Zurich, Switzerland, 16th-20th July, 2007.

Higher order finite difference methods for second order singularly perturbed delay differential equations,
SIAM (Society for Industrial and Applied Mathematics) conference on Computational Science and Engineering,
Costa Mesa, California, U.S.A., 19th-23rd February, 2007.

Higher order methods with suitable mesh for numerical solution of singularly perturbed delay differential equations,
14th International Conference of the Forum for Interdisciplinary Mathematics,
Indian Institute of Technology Madras, 6th-8th January, 2007.